Large cardinals are such cardinals whose existence cannot be proved within ZFC, and requires stronger axioms to be added to ZFC, they are often used to measure the consistency strength of a certain statement in the language of set theory.
Large cardinals are such cardinals whose existence cannot be proved within $\sf ZFC$, and requires stronger axioms to be added to $\sf ZFC$, they are often used to measure the consistency strength of a certain statement in the language of set theory.
For further reading:
- Kanamori, Akihiro. The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings
- Kanamori, Akihiro; Magidor, M., The evolution of large cardinal axioms in set theory
